Turbulence particles not working?
You should add a Force Field. [Shift + A] -> Force Field -> Turbulence



Make sure it's in the same layer as the particles object you want to affect, to get the a turbulent flow of the type you linked.

It looks like what you did was add turbulence to the Particle System in the Force Field Settings tab, which makes each individual particle act as a force field (if you turn on Self-Effect in that tab, you'll see how this affects the particle system).

The Field Weights settings tab controls how much each type of force field affects the particles.